Printer Sharing Issue Loses Connection When Machine Restarted Or Loged Options

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I am having a problems with printer sharing. I have two machines:
1. A desktop with Windows XP Pro service pack 2
2. And a laptop with Windows XP Home service pack 2

There is an HP1020 USB printer connected to the desktop. This printer is shared.

Both machines are connected to a 4-port ADSL router and are both on the same workgroup, and both have their firewalls turned off.

The problem is that the laptop keeps losing connection with the shared printer that is setup on the desktop.

Then you need to reset up the shared printer for it to have access to it again.

Sometimes when it loses connection, when you try set up the shared printer, for some reason you cannot see the shared printer on the network anymore. After awhile it comes back, but at random intervals.

And when you do set up the shared printer again, it seems to lose connection with the printer when you restart or logoff from the laptop

I have tried rebooting the printer to see if this helps at all. And I have tried another router and other network cables to the router.

What could be causing this?

Your help will be much appreciated.